A mapping for a~point spectrum and the uniqueness of a~solution to the inverse problem for a~Sobolev-type equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2010), pp. 55-64.

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In this paper we study a mapping of a point spectrum of a multivalued linear operator that generates a strongly continuous semigroup. We obtain the necessary and sufficient conditions for the uniqueness of a solution to the inverse problem for a Sobolev-type equation.
Keywords: multivalued linear operator, inverse problem, uniqueness of a solution, semigroup of operators, phase field system of equations.
Mots-clés : Sobolev-type equation
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A. V. Urazaeva. A mapping for a~point spectrum and the uniqueness of a~solution to the inverse problem for a~Sobolev-type equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2010), pp. 55-64. http://geodesic.mathdoc.fr/item/IVM_2010_5_a6/

[1] Tikhonov I. V., Eidelman Yu. S., “Teoremy ob otobrazhenii tochechnogo spektra dlya $C_0$-polugrupp i ikh primenenie v voprosakh edinstvennosti dlya abstraktnykh differentsialnykh uravnenii”, Dokl. RAN, 394:1 (2004), 32–35 | MR | Zbl

[2] Favini A., Yagi A., Degenerate differential equations in Banach spaces, Monographs and Textbooks in Pure and Appl. Math., Marcel Dekker, N.Y., 1999, 312 pp. | MR | Zbl

[3] Fedorov V. E., “Lineinye uravneniya tipa Soboleva s otnositelno $p$-radialnymi operatorami”, Dokl. RAN, 351:3 (1996), 316–318 | MR | Zbl

[4] Fedorov V. E., “Vyrozhdennye silno nepreryvnye polugruppy operatorov”, Algebra i analiz, 12:3 (2000), 173–200 | MR | Zbl

[5] Sviridyuk G. A., Fedorov V. E., Linear Sobolev type equations and degenerate semigroups of operators, VSP, Utrecht, 2003, 216 pp. | MR | Zbl

[6] Fedorov V. E., Urazaeva A. V., “An inverse problem for linear Sobolev type equations”, J. Inverse Ill-Posed Probl., 12:4 (2004), 387–395 | DOI | MR | Zbl

[7] Plotnikov P. I., Starovoitov V. N., “Zadacha Stefana s poverkhnostnym natyazheniem kak predel modeli fazovogo polya”, Differents. uravneniya, 29:3 (1993), 461–471 | MR | Zbl

[8] Fedorov V. E., Urazaeva A. V., “Obratnaya zadacha dlya odnogo klassa singulyarnykh lineinykh operatorno-differentsialnykh uravnenii”, Tr. Voronezhsk. zimn. matem. shk., VGU, Voronezh, 2004, 161–172